Catégorie : Collaborations

Abstract : We study the effect of the electron-electron interaction on the weak localization correction of a ring pierced by a magnetic flux. We compute exactly the path integral giving the magnetoconductivity for an isolated ring. The results are interpreted in a time representation. This allows to characterize the nature of the phase coherence relaxation in the ring. The nature of the relaxation depends on the time regime (diffusive or ergodic) but also on the harmonics nn of the magnetoconductivity. Whereas phase coherence relaxation is non exponential for the harmonic n=0n=0, it is always exponential for harmonics nneq0nneq0. Then we consider the case of a ring connected to reservoirs and discuss the effect of connecting wires. We recover the behaviour of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter (compared to the Nyquist length). We also predict a new behaviour when the Nyquist length exceeds the perimeter.

Christophe Texier 1, 2 Gilles Montambaux 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides

Abstract : We consider the weak localization correction to the conductance of a ring connected to a network. We analyze the harmonics content of the Al\’tshuler-Aronov-Spivak (AAS) oscillations and we show that the presence of wires connected to the ring is responsible for a behaviour different from the one predicted by AAS. The physical origin of this behaviour is the anomalous diffusion of Brownian trajectories around the ring, due to the diffusion in the wires. We show that this problem is related to the anomalous diffusion along the skeleton of a comb. We study in detail the winding properties of Brownian curves around a ring connected to an arbitrary network. Our analysis is based on the spectral determinant and on the introduction of an effective perimeter probing the different time scales. A general expression of this length is derived for arbitrary networks. More specifically we consider the case of a ring connected to wires, to a square network, and to a Bethe lattice.

Christophe Texier 1, 2 Gilles Montambaux 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides

Abstract : We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive delta-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or « spin-charge\’\’) separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.

Auteurs

J. N. Fuchs 1 D. M. Gangardt 2 T. Keilmann 3 G. V. Shlyapnikov 2, 4
1 LPS – Laboratoire de Physique des Solides
2 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
3 MPQ – Max-Planck-Institut für Quantenoptik
4 Van der Waals-Zeeman Institute

Abstract : We study the quantum transport through networks of diffusive wires connected to reservoirs in the Landauer-Büttiker formalism. The elements of the conductance matrix are computed by the diagrammatic method. We recover the combination of classical resistances and obtain the weak localization corrections.For arbitrary networks, we show how the cooperon must be properly weighted over the different wires. Its nonlocality is clearly analyzed.We predict a new geometrical effect that may change the sign of the weak localization correction in multiterminal geometries.

Christophe Texier 1, 2 Gilles Montambaux 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides

Abstract : The low temperature magnetoconductance of a large array of quantum coherentloops exhibits Altshuler-Aronov-Spivak oscillations which periodicitycorresponds to 1/2 flux quantum per loop.We show that the measurement of the harmonics content in a square networkprovides an accurate way to determine the electron phase coherence lengthLφLφ in units of the lattice length without any adjustableparameters.We use this method to determine LφLφ in a network realised from a 2Delectron gas (2DEG) in a GaAS/GaAlAs heterojunction. The temperaturedependence follows a power law T−1/3T−1/3 from 1.3 K to 25 mK with nosaturation, as expected for 1D diffusive electronic motion andelectron-electron scattering as the main decoherence mechanism.

Meydi Ferrier 1 Lionel Angers 1 Sophie Gueron 1 Helene Bouchiat 1 Christophe Texier 1, 2 Gilles Montambaux 1 Dominique Mailly 3 Alistair C. H. Rowe 1
1 LPS – Laboratoire de Physique des Solides
2 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
3 LPN – Laboratoire de photonique et de nanostructures

Abstract : We consider graphs made of one-dimensional wires connected at vertices and on which may live a scalar potential. We are interested in a scattering situation where the graph is connected to infinite leads. We investigate relations between the scattering matrix and the continuous part of the local density of states, the injectivities, emissivities and partial local density of states. Those latter quantities can be obtained by attaching an extra lead at the point of interest and by investigating the transport in the limit of zero transmission into the additional lead. In addition to the continuous part related to the scattering states, the spectrum of graphs may present a discrete part related to states that remain uncoupled to the external leads. The theory is illustrated with the help of a few simple examples.

Christophe Texier 1, 2 Markus Buttiker 3
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides
3 Département de Physique Théorique

Abstract : We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of the charge in such graphs out of equilibrium, as well as the distribution of the currents in the wires, inside the graph. These quantities are related to the scattering matrix of the graph. We discuss the case where the graph is weakly connected to the wires.

Christophe Texier 1, 2 Pascal Degiovanni 3
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides
3 Phys-ENS – Laboratoire de Physique de l’ENS Lyon

Abstract : We consider the Friedel sum rule in the context of the scattering theory for the Schrödinger operator −\Dc2x+V(x)−\Dcx2+V(x) on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. The reason for the failure of the Friedel sum rule to count the states is the existence of states localized in the graph and not coupled to the leads, which occurs if the spectrum is degenerate and the number of leads too small.

Auteur

Christophe Texier 1, 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides

Abstract : We present an x-ray diffraction study of the Vanadium-doped blue bronze K0.3(Mo0.972V0.028)O3. At low temperature, we have observed both an intensity asymmetry of the +-2kF satellite reflections relative to the pure compound, and a profile asymmetry of each satellite reflections. We show that the profile asymmetry is due to Friedel oscillation around the V substituant and that the intensity asymmetry is related to the charge density wave (CDW) pinning. These two effects, intensity and profile asymmetries, gives for the first time access to the local properties of CDW in disordered systems, including the pinning and even the phase shift of FOs.

Sylvain Ravy 1 Stephan Rouzière 2 Jean-Paul Pouget 1 Serguei Brazovskii 3
1 LPS – Laboratoire de Physique des Solides
2 School of Chemistry, Physics and Environmental Science
3 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques

Abstract : We consider the scattering theory for the Schrödinger operator −\Dc2x+V(x)−\Dcx2+V(x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.

Christophe Texier 1, 2 Gilles Montambaux 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides